Basically I completly forgotten how to do these stuff, first 3 is to do them and make them as simple as possible, the other two is just to solve the equations.
1) $\displaystyle \displaystyle \frac{x}{6}+\frac{2x}{9}-\frac{x}{3}$
The common denominator is 18. So, amplify the first fraction by 3, the second by 2 and the third by 6.
2), 3)For the next two problems use the properties:
$\displaystyle (a\cdot b)^n=a^nb^n$
$\displaystyle \displaystyle\left(\frac{a}{b}\right)^n\frac{a^n}{ b^n}$
$\displaystyle a^m\cdot a^n=a^{m+n}$
$\displaystyle \displaystyle\frac{a^m}{a^n}=a^{m-n}$
$\displaystyle (a^m)^n=a^{mn}$
$\displaystyle \displaystyle\sqrt[n]{a^m}=a^{\frac{m}{n}}$
4) $\displaystyle ax^2+bx+c=0$
$\displaystyle \displaystyle x_{1,2}=\frac{-b\pm\sqrt{\triangle}}{2a}$, where $\displaystyle \triangle =b^2-4ac$
5) Factorize and then make a table with the sign of each factor, and then use the rule of signs.